Here is the title of a letter from the polymath scientist Dr. Martin Lister published in Philosophical Transactions in 1674 (vol. 9, pp. 96-99).
Note that the phrase "those insects" refers to snails. Yes, back then snails were insects. But that didn't mean that the pioneering scientists of the 17th century thought that snails and insects didn't differ much. Lister et al. were refined enough in that respect—but not in other respects—to know that the 2 groups were sufficiently different. But to them the word insect seems to have had a more inclusive meaning; it meant invertebrate. Therefore, snails were insects.
This usage seems to have continued at least until the end of the 18th century. For example, an anonymous compilation from 1792 titled The natural history of insects had 16 chapters on insects proper.
In addition, there were two chapters on spiders, scorpions, centipes, etc., and one on various worms. Finally, the last one was on snails. In 1792 snails were still insects.
I don't know when the word invertebrate came into use.